Hydrocarbon fluid production wells and similar process flowstreams have a spiral baffle-type separator interposed in a surface flowline for separating fluids of different densities, such as gas from oil or gas from oil and from water, for example. Particulate solids may also be separated from the fluid flowstream. The separator includes a spiral baffle of single or multiple diameters interposed in an elongated cylindrical casing connected at its opposite ends to suitable fittings whereby the separator may be connected to conventional fluid flowlines on the surface just downstream of a wellhead or otherwise in a process flowstream. Multiple spiral baffle separators may be connected in series to provide multiple stages for separation of fluids of different densities. The separator is particularly compact, mechanically uncomplicated and may be easily adapted to be interposed in well production fluid flowlines or conduits for process flowstreams.